An Application of Sinc Sum Function in Hilbert Transformer

Author(s)
Yunlong Wang

Affiliation(s)

Department of Electronic Information Engineering, Huaiyin Institute of Technology, Huaian, China.

Department of Electronic Information Engineering, Huaiyin Institute of Technology, Huaian, China.

Abstract

An application of the sinc sum function in Hilbert transformer (HT) is studied. The expression of the frequency re- sponse of HT is expressed with sinc sum functions. Some properties of sub-amplitude response of HT are proved by using the properties of the sinc sum function. A general HT formula is obtained theoretically and it contains a general window function. As an example three new window functions are obtained. Different from the existing window func- tions obtained from lowpass filters, these window functions are obtained directly from HT. Comparisons show that new windows are better than the Hanning, Hamming, Blackman and Kaiser windows in terms of HT performances.

An application of the sinc sum function in Hilbert transformer (HT) is studied. The expression of the frequency re- sponse of HT is expressed with sinc sum functions. Some properties of sub-amplitude response of HT are proved by using the properties of the sinc sum function. A general HT formula is obtained theoretically and it contains a general window function. As an example three new window functions are obtained. Different from the existing window func- tions obtained from lowpass filters, these window functions are obtained directly from HT. Comparisons show that new windows are better than the Hanning, Hamming, Blackman and Kaiser windows in terms of HT performances.

Cite this paper

Y. Wang, "An Application of Sinc Sum Function in Hilbert Transformer,"*Engineering*, Vol. 5 No. 5, 2013, pp. 1-8. doi: 10.4236/eng.2013.55A001.

Y. Wang, "An Application of Sinc Sum Function in Hilbert Transformer,"

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